KRAGH, Helge - Pierre Duhem, Entropy, And Christian Faith

7/24/2019 KRAGH, Helge - Pierre Duhem, Entropy, And Christian Faith

1/17

379

Pierre Duhem, Entropy, and Christian Faith

Helge Kragh*

The French physicist and polymath Pierre Duhem was strongly devoted to Catholicism but insistedthat science and religion were wholly independent. In an article of 1905 he reflected at length onthe relationship between physics and Christian faith, using as an example the cosmological signif-icance of the laws of thermodynamics. He held that it was unjustified to draw cosmological con-sequences from thermodynamics or any other science, and even more unjustified to draw conse-

quences of a religious nature.I place Duhems thoughts on the physics of a believerin their propercontexts by relating them to the late-nineteenth-century discussion concerning the meaning anddomain of the law of entropy increase. I also consider Duhems position with respect to Catholicscience and culture in the anticlerical Third Republic.

Key words: Pierre Duhem; Ernst Mach; Georges Lematre;Catholicism; neo-Thomism;religion; cosmology; thermodynamics; entropy; heat death.

Life and Work of a Classical Physicist

Pierre Maurice Marie Duhem (18611916, figure 1) was a scientist and scholar of

unusual breadth whose contributions ranged from the history of medieval natural phi-

losophy to mathematical physics.He began his academic career in the 1880s with works

in chemical thermodynamics and continued over the years to develop this branch of

science, intermediary between physics and chemistry, into still more general formula-

tions. Together with Wilhelm Ostwald (18531932), Jacobus Henricus vant Hoff

(18521911), Svante Arrhenius (18591927), and Walther Nernst (18641941), Duhem

counts as one of the pioneers of physical chemistry. In spite of his important contribu-

tions to thermodynamics, electromagnetism, hydrodynamics, and the theory of elastic-

ity, however, he never obtained a university chair in Paris, the absolute center of French

intellectual life. Partly as a result of his disagreements with the scientific and political

establishment, and not least with the powerful chemist and politician Marcelin Berth-

elot (18271907), Duhem had to spend his professional life in the provinces, serving as

lecturer and professor at the universities in Lille, Rennes, and Bordeaux where he

became full professor in 1894. He engaged actively in physics teaching and establishedhimself as an innovative teacher of physics.1 Apart from his scientific and intellectual

work, and the controversies in which he was occasionally involved, Duhems life was

uneventful. He married in 1890, but his wife died two years later, leaving him with their

Phys. perspect. 10 (2008) 3793951422-6944/07/04037917DOI 10.1007/s00016-007-0365-z

* Helge Kragh is Professor at the University of Aarhus, Denmark. His main field of research isthe history of physical science after 1850.


2/17

Helge Kragh Phys. perspect.380

daughter, Hlne (who published a biography of her father in 1936). Duhem died of a

heart attack in 1916, at the age of fifty-five.2

Duhem was politically conservative, strongly anti-Republican, and an orthodox

Catholic. His conservatism extended to the realm of science, at least in the sense that

he resisted the new trends in physics that appeared in the 1890s, beginning with the

discoveries of X rays, radioactivity, and the electron. Having the mind of a classicalphysicist in the French mathematical tradition, and subscribing to the ideals of posi-

tivism (of a kind), he denied the existence of atoms and subatomic particles as real enti-

ties.When quantum theory and the theory of relativity arrived on the scene in the first

decade of the twentieth century, he chose to ignore these new theories. He spelled out

his antiatomism in several works, first in 1892 in the Catholic journal Revue des ques-tions scientifique and ten years later more elaborately in Le mixte et la combinaisonchimique.3 As late as 1913 the year that saw the atomic model of Niels Bohr

Fig. 1. Pierre Maurice Marie Duhem (18611916). Credit: Acadmie des Sciences de lInstitut deFrance.


3/17

Vol. 10 (2008) Pierre Duhem, Entropy, and Christian Faith 381

(18851962) Duhem defended his nonatomistic and nonelectronic view of physicsand chemistry:

The school of the neo-atomists, the doctrines of which center on the concept of the

electron, have again taken up with supreme confidence the method we refuse to fol-

low.This school thinks its hypotheses at last attain the inner structure of matter, that

they allow us to see the elements, as if some extraordinary ultra-microscope were to

enlarge them until they became perceptible to us.We do not share this confidence.

We are not able to recognize in these hypotheses a clairvoyant vision of what there

is beyond sensible things; we regard them only as models.4

In 1915 Duhem gave a series of four lectures on German science at Bordeaux that

severely criticized la science allemande and its roots in what he saw as the deplorable

mindset of the German race.5

In this work of chauvinistic propaganda he describedGerman physicists as good mathematicians who unfortunately were unable to think

intuitively and therefore produced abstract theories with no connection to the real

world: The German, then, quite skillful in the use of the deductive method, but weak-

ly endowed with intuitive knowledge, will multiply the occasions on which the former

may be applied, and restrict as much as possible the circumstances which call for the

latter.6 Duhem had nothing to say about quantum theory, but he mentioned the the-

ory of relativity (meaning the special theory) as a typical example of abstract and ster-

ile German theorizing. Rejecting the principle of relativity as contrary to common

sense, he wrote that it is so plainly a creation of the mathematical mind that one does

not know how to articulate it correctly in ordinary language and without recourse to

algebraic formulas.7 But it, and its abandonment of the classical concepts of space,

time, and motion,does not excite the distrust of German physicists, among whom he

mentioned Albert Einstein (18791955), Hermann Minkowski (18641909), and Max

von Laue (18791960).

Today Duhem is probably best known as a philosopher of science, a reputation pri-

marily based upon his classic book, The Aim and Structure of Physical Theory, firstpublished in 1906.8 Given Duhems lack of appreciation of Einsteinian relativity, it is

ironic that his book influenced Einsteins way of thinking to a considerable degree. It

appeared in German in 1908 as Ziel und Struktur der physikalischen Theorie, translat-ed by Einsteins close friend Friedrich Adler (18791960) and with a sympathetic fore-

word by the famous Austrian physicist and philosopher Ernst Mach (18381916). Ein-

stein read Duhems book, probably in 1909, and it exerted a long and lasting influence

on his epistemological views.What particularly impressed Einstein was the theoretical

holism and the underdetermination of theory choice (often called the Duhem-Quine

thesis) that were central theses in Duhems philosophy of physics. In a letter of 1918,Einstein referred approvingly to the clear book by Duhem. 9

Duhems legacy is not restricted to either his scientific contributions or his work in

philosophy of science. He is recognized as one of the pioneers of the modern history of

science and a founding figure of the scholarly study of medieval natural philosophy. By

a careful study of the notebooks of Leonardo da Vinci (14521519), Duhem was led to

recognize important schools of mathematics and natural philosophy in the late thir-

teenth century and the following two centuries, and he was the first to investigate in


4/17


detail the works of scholastic philosophers such as Jean Buridan (ca. 1300), Albert ofSaxony (ca. 12001280), and Nicole Oresme (ca. 13201382). Duhems pathbreakingwork in the history of science resulted in numerous publications, culminating in his

three-volume tudes sur Lonard de Vinci (19061913) and his ten-volume Systme dumonde (19131959) of which half were published posthumously.When the chair in his-tory of science at the Collge de France had to be filled in 1904, he was asked to put

himself forward as a candidate but refused to have his name placed on the list of can-

didates; if he was to go to Paris, it would be as a physicist. He always insisted that he

was a physicist, not a philosopher or historian of the physical sciences. (The chair was

filled by Grgoire Wyrouboff (18431913), a crystallographer of modest distinction in

the history of science.10)

Like Mach, Duhem used the history of science in support of his philosophical ideas,

for example, in arguing that metaphysics and hidden causes were detrimental to scien-tific progress. He defended a continuity thesis, that progress was (and is) obtained by

the accumulation of empirical knowledge and the gradual refinement of concepts.

According to his understanding of the history of science, the works of the Christian

thinkers in the Middle Ages constituted a break with orthodox Aristotelianism and

thereby paved the way for the later change in natural philosophy that came with

Galileo Galilei (15641642) and his generation. Although Duhems radical continuity

thesis no longer enjoys support among historians of science, in a more moderate ver-

sion it continues to inspire medievalist historians.

Thermodynamics as the Basic Science

Before accounting for Duhems view of the cosmological aspects of thermodynamics, I

must emphasize that he was one of the periods great experts of this science, second

perhaps only to Max Planck (18581947) and J.Willard Gibbs (18391903). But in con-

trast to these physicists, the antiatomist Duhem never accepted the statistical-mechan-

ical view of thermodynamics initiated by James Clerk Maxwell (18311879) and Lud-

wig Boltzmann (18441906). As Louis de Broglie (18921987) later commented:

inspired by a genuine horror of all mechanical or pictorial models, he never became

interested in the interpretation of the abstract concepts of classical thermodynamics,

though it was so instructive and fruitful, which statistical mechanics furnished in his

own lifetime.11

Inspired by the thermodynamical works of Gibbs and Hermann von Helmholtz

(18211894), Duhem developed the theory of chemical potentials (such as the free-

energy functions) in his first book, Le potentiel thermodynamique et ses applications

la mcanique chimique et la thorie des phnomnes lectriques of 1886. His generalmethod, based upon Gibbss work, was to base thermodynamics on the condition that

at equilibrium the potential must be a minimum. Among other things, he considered

systems in which phase changes or chemical reactions take place and wrote the change

in chemical energy as n11 + n22 + + nkk, where the ns refer to the amounts of thecomponents and the s are chemical potentials. According to what is known as the

Gibbs-Duhem equation, n1d1 + n2d2 + + nkdk = 0 for a process taking place atconstant temperature and pressure.12


5/17


Duhem also launched an attack on Berthelots thermochemistry, which was basedupon the assumption that the quantity of heat evolved in a chemical reaction was a

measure of chemical affinity. According to Berthelots principle of maximum work,

first stated in 1864, all chemical reactions are accompanied by heat production, and the

process that actually occurs out of all possible ones is the one in which the most heat

is produced. However, as Duhem argued, this principle was based only upon the law of

energy conservation and failed to take into account the entropy changes given by the

second law of thermodynamics. What Berthelot had stated as a fundamental principle

of science was, according to Duhem, nothing but a ridiculous tautology.13 Berthelot

was not the only chemist who failed to understand the nature and role of entropy; as

late as 1894 he characterized this concept, by then nearly thirty years old, as an

obscure notion and an unknown quantity.14 Duhem emphatically disagreed. He gave

full accounts of the generalized chemical thermodynamics in two monographs pub-lished about the turn of the century, in his two-volume Trait de mcanique chimiques(18971899) and in his Thermodynamique et chimie (1902).

Duhems vision of a generalized thermodynamics (or energetics, as he called it) was

a sort of nonmechanical, phenomenological theory of everything with distinct Aris-

totelian features. It was, he said,not a branch of physics, but the trunk from which sev-

eral subjects branched off. These laws govern all the changes that it is possible to

produce in the inorganic world. 15 He deliberately contrasted the new thermodynam-

ics with the old paradigm of rational mechanics:

Thirty years ago, rational Mechanics still seemed the queen of science of which all

other physical doctrines must be an expression. It was required that Thermodynam-

ics reduce all its laws to mere theorems of Mechanics. Today, rational Mechanics is

no more than the application to a particular problem of locomotion of this generalThermodynamics, of this Energetics whose principles encompass all the transforma-tions of the inorganic world or, according to the peripatetic description, allphysicalmovements.16

Entropy, Heat Death, and Catholic Thought

Shortly after the formulation of the second law of thermodynamics, independently by

William Thomson (18241907) and Rudolf Clausius (18221888) in the early 1850s, it

was applied to the universe at large, first by Helmholtz in an address delivered in

Knigsberg in 1854.17 The essence of the second law, as understood at that time, was

that the energy in a closed system will spontaneously and irreversibly be degraded,

be transformed into a lower-temperature form of heat unable to produce mechanicalwork. As Helmholtz pointed out, the consequence would be a state of equilibrium

scarcely distinguishable from death:Then all possibility of a further change would be

at an end, and the complete cessation of all natural processes must set in. In short,

the universe from that time onward would be condemned to a state of eternal rest.

This scenario of the so-called heat death (Wrmetod) immediately became the subjectof much discussion among both scientists and nonscientists. Thomson formulated the

prediction in terms of dissipation of energy and Clausius framed it in terms of entropy,


6/17


a concept he introduced in 1865. The entropy of the universe tends towards a maxi-mum, he emphasized in a paper of 1868.19 When the state of maximum entropy hadbeen attained, the universe would be dead, never to wake up.

The second law of thermodynamics not only predicted a heat death in the far

future, it also seemed to imply that the world is of finite age and thus had a beginning

in time, since if the universe had existed an eternity ago, the entropy would already

have reached its maximum value, which was clearly not the case. This entropic argu-

ment for a beginning of the universe was introduced in the late 1860s and adopted as

a reasonable hypothesis by leading physicists such as Thomson, Maxwell, and Peter

Guthrie Tait (18311901) who were impressed by its apparent agreement with the

Christian message of a created world.A substantial part of the debate in the late nine-

teenth century was concerned with the apologetic use of thermodynamics and the sig-

nificance of the second law in the ideological and cultural battle that raged throughmuch of Europe at the time. By and large, those in favour of political conservatism,

idealism, and Christian values looked with sympathy to the cosmological claims of

thermodynamics, whereas socialists, materialists, and atheists denied these claims, in

part because they suspected them to be Christian religion masquerading as science.20

The standard argument of the latter group was that the second law was valid only for

a finite collection of bodies and not for the supposedly infinite universe, in which case

their favored worldview of an eternal and cyclical universe did not conflict with the

laws of physics.

The heat death could be avoided even without presupposing an infinite material

universe, namely, by arguing that the inference was methodologically invalid.That was

the position of Mach, who opposed extrapolations of the laws of nature to the entire

universe. His opposition to the heat death was undoubtedly related to his hostility

toward Christian faith.21 In 1871, while professor of physics at Prague,Mach gave a lec-

ture on the history of the principle of energy conservation in which he criticized the

concept of the heat death and its corollary, the origin of the universe, by arguing that

they were scientifically meaningless. It is completely illusory, he wrote, to apply the

second law to the entire universe.This was not because of any problem with Clausiuss

law in particular but because no meaningful statements could be attached to the uni-

verse. Mach argued that, for the statement to be meaningful, we must consider the

object separate from another part of the universe, which acts a clock. But this is impos-

sible for the universe itself, since there is nothing left that can serve as a clock. Theworld is like a machine in which the motion of certain parts is determined by themotion of other parts, only nothing is determined about the motion of the machine asa whole. For the universe there is no [measure of] time.22

During the second half of the nineteenth century the Catholic church was seriouslydisturbed by what came to be known as the modernist crisis,a confrontation between

traditional church dogmas and modern ideas coming from the humanities and natural

sciences. In Bismarcks new, unified Germany the confrontation culminated in a cam-

paign to keep Catholics out of public life and culture, an important element in what is

known as the Kulturkampf. In France, the situation was marked not only by the suc-cessful trend of Comtean positivism but also by the Third Republics sustained anti-

Catholicism and anticlericalism. In 1880 Jesuits and other unauthorized congregations


7/17


were disbanded by law, and this measure was followed by a general offensive againstfaith and church. This campaign reached its climax shortly after the turn of the centu-

ry when Catholic schools were closed and thousands of monks and nuns expelled.

Finally, in 1905 the Republic broke totally with the church and ceased to recognize any

form of religion.Priests and Catholic thinkers responded in a variety of ways, one being

more active participation in scientific, social, and philosophical debates. Part of the

Catholic intellectual counteroffensive was directed against the attempts to use science

as a weapon against religion.23

The Catholic counteroffensive agreed with,and to a large extent was inspired by the

more modernist and reconciliatory strategy of Leo XIII (18101904),pontiff from 1879

to 1904. The Pope actively encouraged scholars to engage in the world of science and

to demonstrate that Catholic thought and modern science were not irreconcilable. In

his widely read History of the Conflict between Religion and Science, the chemist JohnWilliam Draper (18111882) had concluded that Roman Christianity and Science are absolutely incompatible; they cannot exist together; one must yield to the other;

mankind must make a choice it cannot have both.24 The new generation of Catholic

scholars was eager to refute Drapers diatribe and to show that science was not a born

enemy of faith; on the contrary, if supplied with the right metaphysical foundation in

the form of neoscholasticism, science would be a valuable ally of faith.

Neoscholasticism or neo-Thomism, a revised version of the philosophical system of

Thomas Aquinas (12251274), became the foundation of the new Catholic philosophy,

natural philosophy included. Although many Catholic scientists fell for the temptation

to use science apologetically, this was not the aim of neoscholasticism.The Belgian Car-

dinal Desir Joseph Mercier (18511926, figure 2), a leading neo-Thomist and the

organizer of theInstitut Suprieur de Philosophie associated with the Catholic Univer-sity in Louvain, emphasized that the purpose of the new institute was to form, in

greater numbers,men who will devote themselves to sciencefor itself, without any aimthat is professional or directly apologetic.25 Among the professors at the Louvain

institute was Dsir Nys (18591927), who in his youth had studied chemistry under

Ostwald in Leipzig and in Louvain taught courses on cosmology and chemistry. In one

of the volumes of his Cours de philosophie, Nys examined in detail the claim that thesecond law of thermodynamics implied a beginning and an end of the world. He con-

cluded that the law could not be assigned absolute certainty, and for this and other rea-

sons he dismissed its apologetic use and retreated to the safe haven of faith. Did the

world have a beginning? Only faith permits us to respond to this question with com-

plete certainty.26 According to Nys, human reason was unable to provide a definite

proof against the possibility of an eternal world.

Nyss view was in complete agreement with neoscholastic philosophy as expound-ed in the authoritative Manual of Modern Scholastic Philosophy, written by Cardinal

Mercier and several of the professors at the Louvain institute.According to Mercier,

cosmology comprised three parts, namely, (i) the origin of the inorganic world, mean-

ing its first efficient cause; (ii) its intrinsic constitution or ultimate constitutive causes;

and (iii) its destiny or final cause.27 Cosmology in the neoscholastic philosophical tra-

dition thus constituted a much broader subject than the current meaning of the term

with its emphasis on physics and astronomy. It was natural philosophy rather than


8/17


the science of the universe. Mercier and his coauthors were careful not to accept the

thermodynamic argument of the origin of the world as a proof of Gods existence:

But even if science could demonstrate that the actual state of this world as we find

it had a commencement; if the law of entropy could establish as a fact that the

forces of the world have had an origin in far-off ages, reason alone could never be

sure that this state was not endlessly preceded by some other state of which science

is entirely ignorant. In any case it is imprudent to identify the question of the

existence of God with that of the commencement of the world.28

The cautious attitude of leading Catholic philosophers and theologians was not fol-

lowed by all Catholics. In fact, the period from about 1880 to 1910 saw a flood of pub-

lications in which Jesuits and other writers of Catholic faith argued from the second

law of thermodynamics that the world must have had an origin in time and eventually

must come to a standstill. Several of these writers concluded that thermodynamics had

vindicated a divinely created world and thus proved the existence of God.

Fig. 2. Cardinal Desir Joseph Mercier (18511926). Source: Mercier, Manual of Modern ScholasticPhilosophy. Vol. I (ref. 27), frontispiece.


9/17


Physics of a Believer

As a devout and outspoken Catholic scientist, Duhem could not avoid being drawn into

the discussion concerning the relationship among science, philosophy, and theology. While

a professor in Bordeaux,he reflected forcefully on this topic in an important article of 1905

entitled Physics of a believer in theAnnales de philosophie Chrtienne, a Catholic jour-

nal founded in the 1830s. His article received much wider attention when it was included

as an appendix in the second edition of hisAim and Structure of Physical Theory.29

Duhems article was a lengthy response to a detailed and critical essay by the young

philosopher Abel Rey (18731940), who had concluded that Duhems scientific phi-

losophy is that of a believer (note that Rey referred to Duhems philosophy of science,

not his science).30 Although Duhem was indeed a believer, a sincere and fervent

Catholic, he was eager to point out that his works in physics and chemistry should beconsidered on their own merits, independent of his religion.They were not examples of

Catholic science, nor even colored by his Catholic faith. It followed from his posi-

tivistic, antimetaphysical methodology of science that there could be no influence of

religion on science,nor of science on religion (whereas he accepted an influence of sci-

ence on metaphysics). He rejected the idea that arguments from physics, or science in

general, could serve as valid objections against religion, and conversely, that such argu-

ments could support the cause of religion:

Whatever I have said of the method by which physics proceeds, or of the nature and

scope that we must attribute to the theories it constructs, does not in any way prej-

udice either the metaphysical doctrines or the religious beliefs of anyone who

accepts my words. The believer and the nonbeliever may both work in common

accord for the progress of physical science such as I have tried to define it.In itself and by its essence, any principle of theoretical physics has no part to play

in metaphysical or theological discussions.31

In short, Duhem was an ardent advocate of the independence thesis, the view that sci-

ence and religion deal with different realms of reality and therefore can be neither in

conflict nor in harmony.32 Although he firmly believed that the order of nature was

ultimately the work of the Creator, he denied any direct connections between science

and religion based upon natural theology.According to his friend, the Abb Bernies (d.

1929), Duhem held the view that science properly spoken was neither Christian nor

anti-Christian, once it kept itself within its limits. It was simply science. Science and

Revelation have one domain, but absolutely different methods.33

To illustrate his view on the relationship among science, philosophy, and theology,

Duhem referred to the case of thermodynamics, his favorite branch of physics. He firstcommented on the cosmological significance of the laws of thermodynamics in a text-

book of 1897 in which he expressed his disapproval of Clausiuss formulations of the

two laws, which he found to be foreign to physics. According to Duhem, Clausius had

illegitimately applied the laws of thermodynamics to the universe,* which he assimi-

* Duhems reference to Clausiuss view of the universe is puzzling,as Clausius never mentionedthis or any other cosmological model.


10/17


lates to a system of bodies of limited extension and isolated in an absolutely voidspace.34 He repeated his criticism in a later textbook in which he argued that energy

and entropy cannot be uniquely defined for the universe as a whole, irrespective of

whether it is spatially infinite or finite. He therefore concluded that there was no logi-

cal justification for Clausiuss cosmological formulation. More generally:All the philo-

sophical consequences that one believes to be able to derive from an extension of the

principle of energy conservation and the principle of entropy increase to the universe

prove to be an idea that is completely erroneous with respect to the nature and range

of thermodynamics and, in general, the science of physics.35 This methodologically

founded criticism agreed with that of Mach and other scientists of a positivist orienta-

tion.

In his article of 1905, Duhem referred to the entropic argument for creation and

decay, knowing well that this was a controversial subject. He was aware that the lawsof thermodynamics had been used to strengthen the cause of religion, but he consid-

ered this to be based upon a misunderstanding of both physics and Christian religion.

Concerning Clausiuss cosmological version of the second law, he wrote:

From this theorem many a philosopher maintained the conclusion of the impossi-

bility of a world in which physical and chemical changes would go on being pro-

duced forever; it pleased them to think that these changes had had a beginning and

would have an end; creation in time, if not of matter, at least of its aptitude for

change, and the establishment in a more or less remote future of a state of absolute

rest and universal death were for these thinkers inevitable consequences of the prin-

ciples of thermodynamics.36

Duhem, however, did not accept these conclusions, which were marred in more than

one place by fallacies. It followed from his conception of physics that the cosmologi-

cal use of the law of entropy increase was invalid, and also that the law could have no

religious implications. For one thing, the entropic argument implicitly assumes the

assimilation of the universe to a finite collection of bodies isolated in a space absolute-

ly void of matter, he wrote, repeating what he had said in 1897. He saw no reason to

accept this assumption. Moreover, he argued that the entropy law merely says that the

entropy of the universe increases endlessly, not that it has any lower or upper limit:

It is true that the entropy of the universe has to increase endlessly, but it does not

impose any lower or upper limit on this entropy; nothing then would stop this mag-

nitude from varying from to + while the time itself varied from to + ;then

the allegedly demonstrated impossibilities regarding an eternal life for the universe

would vanish.37

Duhems assertion that the second law does not imply that a system will end in a state

of maximum entropy, even if an infinity of time is available, was not original. A simi-

lar argument had been made by Arthur Joachim von Oettingen (18361920), a physi-

cist from the University of Dorpat (now Tartu in Estonia), who in 1876 concluded

that Clausiuss version of the second law was wrong.38 The idea of an asymptotic

increase of entropy was sometimes put forward as an argument against the heat

death, but as pointed out by the Catholic philosopher and theologian Constantin


11/17


Gutberlet (18371928), it did not allow life processes to go on eternally.39 If the uni-verse was in a state of very high entropy, if not in the maximal state, it would still be

dead for all practical purposes.

Duhems aim was certainly not to argue against a universe of finite age, but to warn

that physical theory does not justify such long-term predictions. In this epistemological

respect he was an agnostic (of course, he was not an agnostic in the religious sense).It

is absurd, he declared,to question this theory [thermodynamics] for information con-

cerning events which might have happened in an extremely remote past, and absurd to

demand of it predictions of events a very long way off. It would be a gross miscon-

ception of the scope and nature of science to believe that one could claim for it the

proof of a dogma affirmed by our faith. In agreement with his general philosophy of

science, Duhem pointed out that it would be perfectly possible to construct a new ther-

modynamics that was in agreement with experimental data and gave the same predic-tions as the old thermodynamics for ten thousand years; and yet, the new theory could

be constructed in such a way that it might tell us that the entropy of the universe after

increasing for a period of 100 million years will decrease over a new period of 100 mil-

lion years in order to increase again in an eternal cycle. 40 He definitely did not sub-

scribe to such a strange worldview, but wanted to bring home the point that science is

incapable of making trustworthy predictions about either the beginning or the end of

the world, or its perpetual activity.

Concerning the more general relationship between cosmology and physics, Duhem

claimed that the two fields are so different that physical theory cannot be applied

meaningfully to cosmology. He did not deny that knowledge of physics can be useful,

and even indispensable for the cosmologist, but he argued nonetheless that physical

theory can never demonstrate or contradict an assertion of cosmology, for the propo-

sitions constituting one of these doctrines can never bear on the same terms which the

propositions forming the other do, and between two propositions not bearing on the

same terms there can be neither agreement nor contradiction. 41 The only connection

of cosmology to theoretical physics was by means of analogy. Duhems denial of the

possibility of physical cosmology may appear surprising, but one should be aware that

he spoke of cosmology mostly in a philosophical, neoscholastic sense of the word.

The cosmology of Aristotelian physics was, he said, unmistakably analogous to gen-

eralized thermodynamics.

The Catholic Context

Thefin de sicle ideology in France was colored in part by a growing revolt against pos-

itivism, scientism and the agnostic-materialistic ideas that the scientific worldview wasaccused of fostering. In early 1895 the French literary critic and orthodox Catholic Fer-dinand Brunetire (18491906), inspired by a visit to the Vatican, published an article inwhich he attacked positivistic science and argued that it had failed to answer, or evenaddress the greater questions of matter and life. In the heated debate that followed,some critics of science proclaimed the bankruptcy of science (Brunetire himself didnot use this phrase, but spoke only of the failure of science).42 Nor was it only in Francethat science was charged with being morally bankrupt. The Irish writer and Victorian


12/17


feminist Frances Power Cobbe (18221904) wrote in 1888 that a man bred to sciencewill view his mothers tears not as expressions of her sorrow, but as solutions of muri-ates and carbonates of soda, and of phosphates of lime;and he will reflect that they werecaused not by his selfishness, but [by] cerebral pressure on her lachrymal glands.43

Contrary to what preachers of the scientific gospel claimed, positivistic science was

widely held to be inferior to religion because it provided no insight into the supreme

mysteries of the universe, or into the mysteries of the meaning of love, life, and death.

In this intellectual climate, French Catholics eyed an opportunity to come back on the

scene, not only as critics of scientistic tendencies but also as interpreters of and con-

tributors to science. Jesuit scholars engaged in the history of science to demonstrate

that a substantial part of the progress of science was due to the work of scientists of

Catholic faith.44

Duhem was very much his own man. His ideas, whether scientific, political, or reli-gious, conflicted sharply with those held by the cultural and scientific elite of France.

Although he was a fervent supporter of Catholicism, he was far from representative of

Catholic scientists, most of whom had no problems with arguing apologetically, that is,

to the effect that science supported Christian theology. For example, in 1905 the

Catholic geologist Albert de Lapparent (18391908) gave a series of lectures that was

published as Science et apologtique and whose message was that that recent develop-ments of science were fully congruent with Christian faith. Contrary to Duhem, Lap-

parent believed that the idea of a beginning and an end of the universe could be given

scientific support:The [Christian] idea of origin and end applied to the entire creation

seems to find a remarkable confirmation in the fundamental law of this energetics in

which all the sciences of matter tend more and more to meet.45

While Duhem emphatically declined to use science apologetically, he saw his

research in the history of medieval science in a different light. The study of the history

of science would show, he wrote, that during those very ages when men cared above

all for the kingdom of God and of its justice, God accorded to them as a bonus the most

profound and fertile thoughts concerning matters down here.46 In the second volume

of his book, The Origins of Statics of 1906, he wrote about the many attempts in theMiddle Ages to establish a science of statics that demonstrated the existence of a divine

architect:

How could all these efforts combine with such precision and bring to completion a

plan which was not known to the individual laborer, unless this plan existed previ-

ously in the mind of an architect, and if this architect did not have the power to

direct and coordinate the labor of all the masons? Even more than the growth of a

living being, the evolution of statics is the manifestation of the influence of a guid-

ing idea.Within the complex data of this evolution, we can see the continuous action

of a divine wisdom which foresees the ideal form towards which science must tend

and we can sense the presence of a Power which causes the efforts of all thinkers to

converge towards this goal. In a word, we recognize here the work of Providence.47

Although natural theology had no place in Duhems conception of science, it went

hand in hand with the history of science.This may seem rather surprising, if not incon-

sistent. After all, todays science is tomorrows history of science.

Lgica da cincia e teorias fsicas X histria das cincias

A histria da cincia

apologtica, ape-

sar de as teorias no

o serem.


13/17


According to Duhem, the controversy between Catholic thought and modern sci-ence was essentially a misunderstanding based upon a failure to appreciate the sepa-

rate domains of the two fields. He had nothing but disdain for the many words wasted

on the subject:

It has been fashionable for some time to oppose the great theories of physics to the

fundamental doctrines on which spiritualistic philosophy and the Catholic faith rest;

these doctrines are really expected to be seen crumbling under the ramming blows

of scientific systems. Of course, these struggles of science against faith impassion

those who are very poorly acquainted with the teachings of science and who are not

at all acquainted with the dogmas of faith; but at times they preoccupy and disturb

men whose intelligence and conscience are far above those of village scholars and

caf physicists.48

Duhems views were controversial, both within the state university system and within

the Catholic church. As an indiscreet Catholic, his career was deeply affected by the

hostility of anticlerical governments toward Catholicism.49 As an independent mind,

his insistence on a sharp separation between science and faith made him a target of

some Catholics who suspected him of philosophical scepticism and fideism, the

heretical belief that faith rests upon faith and nothing else. Not only was his view con-

cerning science and religion problematical, so was his philosophy of science, primarily

because it was radically antimetaphysical and seemed to undermine natural theology.50

Among Duhems later critics was the influential neo-Thomist philosopher Jacques

Maritain (18821973), who objected to Duhems philosophy of physics and especially

its independence of any metaphysical framework,Thomism included.

Bernard Brunhes (18671910), Professor of Physics and Director of the Observato-

ry at Puy-de-Dme, had a high regard for Duhem and his philosophy of physics. In 1908

he published an excellent and comprehensive review of the second law of thermody-

namics entitled La dgradation de lnergie, but he chose not to include its wider cos-mological and religious aspects.The Catholic Brunhes was not foreign to these aspects,

but, like Duhem,he wanted to keep them separate from scientific aspects.51 Like many

other Catholic scientists, Brunhes kept a low profile in matters of religion, aware that

controversial statements concerning science and Christian faith might annoy the

Republican establishment and harm his career. Although this was not Duhems style,

he agreed that thermodynamics had no religious implications.

Conclusion: Duhem and Lematre

Duhems refusal to accept, or even take seriously the metaphysical and religious con-sequences of thermodynamics, such as the beginning of the universe in a state of low

entropy, was not particularly unusual for a Catholic scientist. As mentioned, leading

Catholic philosophers and theologians shared the view that physics cannot prove the

finiteness of the age of the world and even less its divine creation. Yet Duhems rea-

sons for dismissing cosmological thermodynamics were different, as they were rooted

in his general philosophy of physics. According to his philosophy, theories of physics

are mathematical representations rather than explanations. As such, they are neither


14/17


true nor false but merely convenient statements that more or less completely andexactly cover groups of phenomena;a finite number of phenomena or data may be rep-

resented by many different theories. By their very nature, then, theories of physics are

noncosmological and therefore also irrelevant to religious faith.

Of course, Duhem is not the only Catholic scientist who has subscribed to the inde-

pendence thesis. So did the Belgian priest and pioneer of modern cosmology Georges

Lematre (18941966). Although he did not share Duhems view that physics is of no

direct cosmological relevance, he did agree that science and religion are different and

autonomous ways of knowing. Speaking of the big-bang model of the universe at the

eleventh Solvay conference in 1958, Lematre said: As far as I can see, such a theory

remains entirely outside any metaphysical or religious question. It leaves the material-

ist free to deny any transcendental Being. He may keep, for the bottom of space-time,

the same attitude of mind that he has been able to adopt for events occurring in non-singular places in space-time. 52 This was a view entirely in agreement with what

Duhem had written in Physics of a believer. Lematre, however, did not dismiss the

entropic creation argument for philosophical or other reasons. In fact, the law of

increase of entropy played a significant role in the thinking that led him to propose the

big-bang model of the universe in 1931.53

As mentioned, at the time of Duhem the heat death was a controversial and much

discussed issue.Does the second law of thermodynamics apply to the universe at large?

Does it lead to a dead universe in the far future? One year after Duhems death, Ein-

stein revolutionized cosmology by basing it upon the field equations of general rela-

tivity, and since then cosmology has developed into an advanced science of which

Duhem and his contemporaries could scarcely dream. Contrary to what one might

believe, the rapid progress in physical cosmology has not led to a clarification of the

thorny question of cosmic entropy. On the contrary, this entire question rather has

become more complicated and muddled. Few modern cosmologists believe that the

second law is valid for the universe in any straightforward way. It is far from clear how

to apply thermodynamics to a universe governed by classical general relativity,or if the

notion of the entropy of the universe is at all well-defined. I see no reason to expect

that there will be a meaningful notion of the total entropy of the universe, says

Robert M. Wald, a leading expert on cosmology and thermodynamics. Nevertheless,he

believes that in (quantum) general relativity some notion of entropy will exist and the

basic form of the laws of thermodynamics will survive. 54

Acknowledgment

I thank Roger H. Stuewer for his careful editing of my manuscript.

References

1 Michael J. Crowe, Pierre Duhem, the History and Philosophy of Physics, and the Teaching ofPhysics, Physics in Perspective 1 (1999), 5464.

2 For biographical accounts of Duhem, see Stanley Jaki,Uneasy Genius:The Life and Work of PierreDuhem (The Hague:Martinus Nijhoff,1984);Donald G. Miller,Ignored Intellect:Pierre Duhem,


15/17


Physics Today 19 (December 1966), 4753; Donald G. Miller, Duhem, Pierre-Maurice-Marie, inCharles Coulston Gillispie, Editor in Chief,Dictionary of Scientific Biography, Vol. 4 (New York:Charles Scribners Sons, 1971), pp. 225233; Hlne Pierre-Duhem, Un savant franais: PierreDuhem (Paris: Plon, 1936).

3 Pierre Duhem, Notation atomique et hypothse atomistiques, Revue des questions scientifique31 (1892),391457; translated by Paul Needham as Atomic Notation and Atomistic Hypotheses,Foundations of Chemistry 2 (2000), 127180. Pierre Duhem, Le mixte et la combinaison chimique:Essai sur levolution dune ide (Paris: C. Naud, 1902), translated and edited by Paul Needham asMixture and Chemical Combination and Related Essays (Dordrecht: Kluwer Academic, 2002).

4 Pierre Duhem, Notice sur les titres et travaux scientifique de Pierre Duhem (Bordeaux: Gounouil-hou, 1913), p. 71; quoted in Robert J.Deltete and Anastasios Brenner,Essay Review [of Duhem,Mixture and Chemical Combination (ref. 3)], Found. Chem. 6 (2004), 201230, on 224225.

5 Pierre Duhem, La science allemande (Paris:A. Hermann et Fils, 1915); translated by John Lyon asGerman Science (La Salle, Ill: Open Court, 1991). See also Harry W. Paul, The Sorcerers Appren-tice: The French Scientists Image of German Science, 18401919 (Gainesville: University of Flori-

da Press, 1972).6 Duhem, La science allemande (ref. 5), p. 12.7 Ibid., p. 105.8 Pierre Duhem,La thorie physique,son objet,sa structure (Paris:Chevalier et Rivire, 1906); trans-

lated by Philip P. Wiener as The Aim and Structure of Physical Theory (Princeton: Princeton Uni-versity Press,1954; New York:Atheneum, 1974).

9 Quoted in Don Howard,Einstein and Duhem, Synthese 84 (1990), 363384, on 368.10 Harry W. Paul, Scholarship versus Ideology: The Chair of the General History of Science at the

Collge de France, 18921913,Isis 67 (1976), 376398.11 Louis de Broglie,Foreword, in Duhem,Aim and Structure (ref. 8), p. x.12 On the development of chemical thermodynamics, see Varadaraja V. Raman,The Permeation of

Thermodynamics into Nineteenth Century Chemistry,Indian Journal for History of Science 10(1975), 1637; James R. Partington,A History of Chemistry, Vol. 4 (London: Macmillan & Co.,1964), pp.608636.

13 Pierre Duhem, Thermochimie, Revue des questions scientifique 12 (1897), 361392, on 370. Forthe controversy over Berthelots thermochemistry, see R. G.A. Dolby, Thermochemistry versusThermodynamics:The Nineteenth Century Controversy, History of Science 22 (1984), 375400.

14 Marcelin Berthelot, Le principe du travail maximum et lentropie, Comptes rendus hebdo-madaires des sances de lAcadmie des Sciences 118 (1894), 13781392, on 1385. See also HelgeKragh and Stephen J.Weininger, Sooner Silence than Confusion:The Tortuous Entry of Entropyinto Chemistry, Historical Studies in the Physical Sciences 27 (1996), 91130.

15 Duhem, Mixture and Chemical Combination (ref. 3), p. 109.16 Ibid.17 Hermann von Helmholtz,On the Interaction of the Natural Sciences [1854], inScience and Cul-

ture: Popular and Philosophical Essays, edited by David Cahan (Chicago and London:Universityof Chicago Press, 1995), pp.1845.

18 Ibid., p. 30.19 R. Clausius, On the Second Fundamental Theorem of the Mechanical Theory of Heat; a Lecture

delivered before the Forty-first Meeting of the German Scientific Association,at Frankfort on theMaine,September 23, 1868, Philosophical Magazine 35 (1868),405419,on 419; italics in the orig-inal.

20 Raymond J. Seeger,On Humanistic Aspects of Entropy,Physis 9 (1969), 215234;Helge Kragh,Matter and Spirit in the Universe.Scientific and Religious Preludes to Modern Cosmology (London:Imperial College Press, 2004), pp. 5069; Elizabeth R. Neswald, Thermodynamik als kulturellerKampfplatz: Zur Faszinationsgeschichte der Entropie 18501915 (Berlin: Rombach Verlag, 2006).

21 John T. Blackmore, Ernst Mach: His Work,Life,and Influence (Berkeley:University of CalfiforniaPress, 1972), pp.235, 290292.

22 Ernst Mach, Die Geschichte und die Wurzel des Satzes von der Erhaltung der Arbeit(Leipzig:J. A.Barth,1909), pp. 3637.


16/17


17/17


49 Paul, The Crucible and the Crucifix (ref. 23); Miller, Ignored Intellect (ref. 2); Jaki, UneasyGenius (ref. 2).

50 Paul, Edge of Contingency (ref. 23); R.N.D. Martin, Pierre Duhem: Philosophy and History in theWork of a Believing Physicist(La Salle, Ill.: Open Court, 1991), pp.203207.

51 Bernard Brunhes, La dgradation de lnergie (Paris: Ernest Flammarion, 1908); idem, La portedu principe de la dgradation de lnergie,Annales de philosophie chrtienne 1, no. 151 (1905),582602; ibid., no.152 (1905), 2748.

52 Georges Lematre,The Primaeval Atom Hypothesis and the Problem of the Clusters of Galax-ies,in R. Stoops,ed., La structure et lvolution de lunivers (Brussels: Coudenberg, 1958), pp.125,on p. 7.

53 Helge Kragh and Dominique Lambert,The Context of Discovery:Lematre and the Origin of thePrimeval-Atom Universe,Annals of Science 64 (2007), 445470.

54 Robert M.Wald,The arrow of time and the initial conditions of the universe,Studies in Historyand Philosophy of Modern Physics 37 (2006),394398,on 396. See also Steven Frautschi,Entropyin an Expanding Universe, Science 217 (1982), 593599.

Steno InstituteBuilding 1521University of Aarhus8000 Aarhus, Denmarke-mail: [email protected]

KRAGH, Helge - Pierre Duhem, Entropy, And Christian Faith

Documents

Transcript of KRAGH, Helge - Pierre Duhem, Entropy, And Christian Faith